Hi,
Interesting idea -- kind of like a small batch heater, but simpler to build.
The ID of 3/4 pex is 0.671 inches, so 300 ft of 3/4 pex holds:
(0.671)^2*0.785*12*300/231 = 5.5 gallons -- so, best make that shower fairly quick
I'd use polyiso insulation rather than the pink xps -- its very easy to melt the xps -- I've made a lot of xps thermal sculptures
I think that the 4 inches is probably overkill -- no matter what you do to the back, the front is still only R2, so once you get the back up to (say) R8, nearly all the heat is being lost out the front.
I did a PEX collector:
The $1000 Solar Water Heating System
This worked fine, but even with a tilt of 70 degrees (nearly vertical), and only single glazing, there were times when the collector temperature got up to 230F. You will really have to keep an eye on the stagnation temperature in the summer and fall. In my collector, the PEX was not pressurized, so 230F once in a while was OK, but in your case the PEX will be under full mains pressure, and you will have to keep the temperature lower.
If you have not bought your PEX yet, PEXUniverse.com has good prices and free shipping -- $115 (I think) for 300 ft of 3/4.
Gary